In general, it is known that, in a servo-system, the modes of operation of certain elements are necessarily different. For example, the mode of the control element should be performed in a frequency range much higher than that of the mode of the controlled process.
As a consequence, the fundamental problem of a damping system is to assure a sufficient stability for the base mode, for example, the mode in which the process evolves (when this evolves in a very large domain) without this destabilizing one or more antagonistic modes, namely the high frequency modes. The ideal would be to be able to detect logarithmic decrements of these modes and to regulate them to remain greater than or equal to certain pre-determined values. However, experience shows that it is not easy to detect the dampings correctly for systems having multiple modes or when the initial conditions are of any values whatever.
In order to try to obtain these results, a number of solutions have been advanced, but these solutions have never given complete satisfaction. Among these solutions can be cited firstly the method of frequency detection. This solution appears to be very attractive from the theoretical viewpoint, but is found to be realizable only with great difficulty in practice and even unobtainable in certain cases because the frequency of a power member, affected by non-linearity, is undefinable.
Another solution consists of the utilization of passive adaptive "non-linear" systems. The study and the realization of these systems, however, have shown a number of weaknesses. For example because of "passivity" due to the freezing of their regulation, these systems have poorer performance than "active systems" which effect a proper change of parameter.
There can also be mentioned systems having reference models which require intentional load or test integration to identify the process course, that is to say to determine the value of the variable parameters in the domain of operation of the process course in order to realize the necessary corrections.
These systems have the disadvantage of imposing a certain proper frequency and a damping which is unacceptable in a number of processes in which it is undesirable for the proper frequency to be identical in all regimes of operation. Additionally, these systems require, as a consequence a substantial control energy for a great variation of the parameter.